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Anonymous asked in Science & MathematicsMathematics · 2 months ago

# what is the equation of a line in slope-intercept form that is perpendicular to the line y=-3x+2 and passes through (3,-1)?

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Perpendicular lines have negative-reciprocal slopes.  The slope of the first line is -3 so the slope of its perpendicular is 1/3.

We have the slope, an x, and a y so we can solve for the unknown intercept:

y = mx + b

-1 = (1/3)(3) + b

-1 = 1 + b

-2 = b

y = (1/3)x - 2

• Start with point-slope form. The slope of a perpendicular line is the negative reciprocal of the slope of the original line.

So,y+1=1/3(x-3)

y+1=(1/3)x-1

y=(1/3)x-2

• y = - 3x + 2

solving the slope that is perpendicular to y = - 3x + 2

m = - 3

m2 = - 1/(-3) = 1/3

solving for y - intercept using slope intercept form formula.

y = mx + b

- 1 = 1/3(3) + b

- 1= 1 + b

b = - 1 - 1

b = - 2

The equation of the line that is perpendicular to y = - 3x + 2 is

y = 1/3x - 2  Answer//

• Any line perpendicular to y = -3x+2 must have slope m = ¹⁄₃

The equation of a line with slope m = ¹⁄₃ and passing through (3,-1) is

y - (-1)  = ¹⁄₃ (x - 3)

y = ¹⁄₃ x - 2   .......................ANS • The typical equation of a line is: y = mx + y₀ → where m: slope and where y₀: y-intercept

y = - 3x + 2 ← this is the line (ℓ₁) → the slope is (- 3)

Two lines are perpendicular if the product of their slope is (- 1).

As the slope of the line (ℓ₁) is (- 3), the slope of the perpendicular line (ℓ₂) is (1/3).

The equation of the perpendicular line (ℓ₂) becomes: y = (1/3).x + y₀

The line (ℓ₂) passes through (3 ; - 1), so the coordinates of this point must verify the equation of the line (ℓ₂).

y = (1/3).x + y₀

y₀ = y - (1/3).x → you substitute x and y by the coordinates of the point (3 ; - 1)

y₀ = - 1 - [(1/3) * 3]

y₀ = - 1 - 1

y₀ = - 2

The equation of the line (ℓ₂) is: y = (1/3).x + 2

• y = x/3 + c

-1 = 3/3 + c

y = x/3 - 2

• The perpendicular gradient is the negative reciprocal of '-3' , which is '1/3'

Displacing the point against (x,y)

y - - 1 = (1/3)(x - 3)

y + 1 = x/3 - 3/3

y + 1 = x/3 - 1

y = x/3 + 2  or y = (1/3)x  + 2